 From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.  Elements of Plane Geometry - Page 177by Franklin Ibach - 1882 - 196 pagesFull view - About this book
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...=2ac+62. COR. From this proposition it is evident, that the square described on the difference oftwo lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a—c=A ; therefore, by involution,... | |
 | Nathan Scholfield - 1845 - 894 pages
...which a line may be divided. This is equivalent to the algebraical expression PROPOSITION XI. THEOREM. The square described on the difference of two lines...equivalent to the sum, of the squares described on the lines, minus twice the rectangle contained by the lines. Let AB and BC be two lines, AC their difference... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
....-.a2+c2=62+2c(6+c), « or a2+c2=2ac+62. COR. From this proposition it is evident, that the square described on tJte difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b ; therefore, by... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...«2+c2=i2+2ic+2c2 ; .-. a'2+c'2=b'2+Zc(b+c), or a2+c2=2ac+i2. COR. From this proposition it is evident, that the square described on the difference of two...equivalent to the sum of the squares described on (he lines respectively, minus twice the rectangle contained by the lines. For a — c=b ; therefore,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...Scholium. This proposition is expressed algebraically thus: (a+b)'=a'+2ab+V. PROPOSITION IX. THEOREM. The square described on the difference of two lines, is equivalent to the sum of the squares of the lines, diminished by twice the rectangle contained by the lines. squares on AB and CB, diminished... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...that product. THEOREM XI. If a line be divided into two parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. . Let the line AB be divided into... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...that product. THEOREM XI. If a line be divided into two parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...algebra, in obtaining the square of a binomial ; which is expressed thus : D II PROPOSITION IX. THEOEEM. The square described on the difference of two lines, is equivalent to the sum of the squares descr1bed on the lines, diminished by twice the rectangle contained by the lines. Let AB, BC, be two... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...half that productTHEOREM XIIf a line be divided into two parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle container! by the parts Let the line AB be divrled into two... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...<z2-f-c2=42--2c(4+c), or a2+c2=2ac-f-42. COR. From this proposition it is evident, that the square aescribod on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b ; therefore, by... | |
| |
